Highest Common Factor of 610, 235, 904 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 610, 235, 904 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 610, 235, 904 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 610, 235, 904 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 610, 235, 904 is 1.

HCF(610, 235, 904) = 1

HCF of 610, 235, 904 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 610, 235, 904 is 1.

Highest Common Factor of 610,235,904 using Euclid's algorithm

Highest Common Factor of 610,235,904 is 1

Step 1: Since 610 > 235, we apply the division lemma to 610 and 235, to get

610 = 235 x 2 + 140

Step 2: Since the reminder 235 ≠ 0, we apply division lemma to 140 and 235, to get

235 = 140 x 1 + 95

Step 3: We consider the new divisor 140 and the new remainder 95, and apply the division lemma to get

140 = 95 x 1 + 45

We consider the new divisor 95 and the new remainder 45,and apply the division lemma to get

95 = 45 x 2 + 5

We consider the new divisor 45 and the new remainder 5,and apply the division lemma to get

45 = 5 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 610 and 235 is 5

Notice that 5 = HCF(45,5) = HCF(95,45) = HCF(140,95) = HCF(235,140) = HCF(610,235) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 904 > 5, we apply the division lemma to 904 and 5, to get

904 = 5 x 180 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 904 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(904,5) .

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Frequently Asked Questions on HCF of 610, 235, 904 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 610, 235, 904?

Answer: HCF of 610, 235, 904 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 610, 235, 904 using Euclid's Algorithm?

Answer: For arbitrary numbers 610, 235, 904 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.